Question

The cost of painting the whole surface area of a cube at the rate of 13 paisa per $c{m^2}$ is Rs. 343.98, then the volume of the cube is ____
A) $6859c{m^3}$
B) $8000c{m^3}$
C) $9261c{m^3}$
D) $10.648c{m^3}$

Answer 1

Hint: Convert 343.98 rupees into paisa. Divide the total cost painting the surface area by 13. You will get the total surface area of the cube. By equating the surface area with its value, you will get the length of the side of the cube. Using the side length find the volume of the cube.

Complete step-by-step answer:
We are given that the cost of painting the whole surface area of a cube is Rs. 343.98 at rate of 13 paisa per $c{m^2}$
$
  1rupee = 100paisa \\
  Rs.343.98 = ?paisa \\
   = 343.98 \times 100 \\
   = 34398paisa \\
 $
Total surface area= Cost of painting total surface area/cost of painting 1 $c{m^2}$ of area
$
   = \dfrac{{34398}}{{13}} \\
   = 2646c{m^2} \\
 $
Total surface area of the cube is $2646c{m^2}$
Total surface area formula of a cube is $6{l^2}$ where ‘l’ is the length of the side of a cube.
$
  6{l^2} = 2646 \\
  {l^2} = \dfrac{{2646}}{6} \\
  {l^2} = 441 \\
  l = \sqrt {441} \\
  l = \sqrt {{{21}^2}} \\
  l = 21cm \\
 $

Volume of a cube is ${l^3}$
L=21cm
Volume of the cube with side 21cm is
$
   = {l^3} \\
   = l \times l \times l \\
   = 21 \times 21 \times 21 \\
   = 9261c{m^3} \\
 $
Therefore, the volume of the cube is $9261c{m^3}$
From among the options given in the question Option C is correct, which is the volume of the cube with side 21cm is $9261c{m^3}$

Note: A cube, three-dimensional figure, has equal length, breadth and height which mean 6 equal square sides. A cube has 6 faces, 12 edges and 8 vertices. Volume always must be cubic units.